CN114692397A - Cluster distributed capture method based on multi-mechanism combination strategy - Google Patents

Abstract

The invention discloses a cluster distributed capture method based on a multi-mechanism combination strategy, which comprises the steps of constructing an confrontation scene and a kinematics model of a chaser and an escaper, constructing a multi-mechanism capture strategy of the chaser according to the confrontation scene and the kinematics model, constructing a multi-target optimization function according to the multi-mechanism capture strategy of the chaser, introducing an analytic hierarchy process to distribute weights for the multi-target optimization function, solving the multi-target optimization function by using a particle swarm algorithm, outputting a solution result as the strategy of the chaser, and the like. The method has simple and distinct behavior strategies, does not need complex modeling derivation, has simple and convenient algorithm, does not need complex hyper-parameter adjustment and long-time training process, and has rapid deployment capability; in the case of limited communication and processing capabilities, task capabilities better than centralized control may be exerted; the constructed model is fast in solving speed under the resolving of the particle swarm algorithm, and the real-time requirement can be met. The invention is widely applied to the technical field of intelligent agent pursuit and escape control.

Description

Cluster distributed capture method based on multi-mechanism combination strategy

Technical Field

The invention relates to the technical field of intelligent agent pursuit and escape control, in particular to a cluster distributed capture method based on a multi-mechanism combination strategy.

Background

Tasks such as unmanned aerial vehicle group search and rescue tasks, contaminated target object cleaning tasks, missile or satellite interception tasks and the like can correspond to the pursuit model, for example, an unmanned aerial vehicle in the unmanned aerial vehicle group search and rescue tasks is equivalent to a pursuit catcher, a searched and rescued object is equivalent to an escaper, an intercepted missile or satellite is equivalent to an escaper, and a missile which is launched out for interception is equivalent to a pursuit catcher, so that a good pursuit or catching algorithm is designed, and the completion efficiency of the tasks is favorably improved, such as the unmanned aerial vehicle group search and rescue efficiency, the contaminated target object cleaning efficiency and the missile or satellite interception efficiency.

At present, most of research on the pursuit escape problem is concentrated on a small number of individuals, namely one individual and two individuals, but the pursuit escape problem in reality generally comprises a plurality of individuals, for example, a plurality of unmanned aerial vehicle search and rescue missing persons are dispatched, and a plurality of pursuits and escapers are involved, at the moment, the research on the pursuit escape problem is easy to fall into a multidimensional trap, and the corresponding analysis countermeasure is difficult to solve in the prior art.

Currently, methods such as dynamic programming, gradient algorithm, reinforcement learning, etc. are used to obtain numerical solutions or approximate solutions of multiple body pursuit problems, and methods based on reinforcement learning are gradually attracting attention in the research of pursuit problems, and intelligent bodies learn to high-yield strategies using algorithms such as Deep Q-network (DQN), Fuzzy Actor Criticality Learning (FACL), Deep Deterministic Policy Gradient (DDPG), and double delayed Deep deterministic policy gradient (TD 3). However, applying the above-mentioned technology related to artificial intelligence will face complex modeling derivation, hyper-parameter tuning, and long-time training process, and have high requirements on hardware performance such as data processing capability, communication delay, bandwidth, and the like, so that the problems of poor real-time performance, slow deployment, and the like easily occur.

Disclosure of Invention

Aiming at least one technical problem of poor real-time performance, slow deployment and the like of the existing escape problem solving technology, the invention aims to provide a cluster distributed capture method based on a multi-mechanism combination strategy, which comprises the following steps:

constructing a confrontation scene of a chaser and an escaper; the chaser and the escaper are both intelligent agents;

establishing a kinematic model of the chaser and the escaper;

constructing a multi-mechanism capture strategy of a chaser according to the confrontation scene and the kinematics model;

constructing a multi-objective optimization function according to the multi-mechanism capture strategy of the chaser, and introducing an analytic hierarchy process to distribute weights for the multi-objective optimization function;

and solving the multi-objective optimization function by using a particle swarm algorithm, and outputting a solving result as a strategy of the chaser.

Further, the cluster distributed capture method based on the multi-mechanism combination strategy further includes:

constructing an optimized model of an escaper by an artificial potential field method;

and solving the optimized model of the escaper by using a particle swarm algorithm to obtain a solution result as the strategy output of the escaper.

Further, the confrontation scenario includes:

catch up person P _i1,2,3,.., N, escaper E, starting point (x)_start,y_start) Target point (x)_target,y_target) And a countermeasure area Ω_A；

The maximum speed v of the chaser_p,maxThe maximum velocity of the escaper is v_e,maxBoth running at maximum speed and having v_p,max<v_e,max；

The number of the chaser individuals is N, the number of the escaper individuals is 1, and N is more than 1;

the perception radius of the chaser is r_p,maxRadius of perception of escaper is r_e,maxHas r of_p,max＝r_e,maxAnd both the pursuit and the evasion parties can acquire the position coordinates and the speed vectors of the individuals of the opposite party in the self-perception range through perception;

the most effective is the chasing oneLarge angular velocity limit omega_p,maxThe maximum angular velocity of the escaper is limited to ω_e,maxHas omega_p,max＝ω_e,max；

The chaser has communication distance limitation with r as the communication radius_p,comHas r of_p,com＝2·r_p,maxAnd the chaser can mutually acquire position coordinates and speed vectors with neighbors in a communication range;

the catching radius of the chaser is r_p,capThe warning radius of the escaper is r_alert。

Further, the kinematic model includes:

wherein x is_pi＝(x_pi,y_pi) To catch person P_iCoordinate of (v)_piTo catch person P_iSpeed of (e), ω_piTo catch person P_iThe angular velocity of (a) of (b),

to catch person P_iYaw angle of, chasing person P_iIs expressed as

v_pi∈[0,v_p,max]，|ω_pi|≤ω_p,max；x_e＝(x_e,y_e) As the coordinate of the escaper E, v_eSpeed of the escaper E, ω_eThe angular velocity of the escaper E, phi the yaw angle of the escaper E, and the state quantity of the escaper E is represented as X_e＝{x_e,y_e,φ}，v_e∈[0,v_e,max]，|ω_e|≤ω_e,max。

Further, the pursuit multi-mechanism catching strategy comprises a core mechanism and an auxiliary mechanism; the core mechanism includes an angle reduction mechanism, a distance reduction mechanism, and a structure contraction mechanism, and the auxiliary mechanism includes a collision mechanism, an overlay mechanism, and an edge mechanism.

Further, the angle reduction mechanism includes:

behavior trend function V_θ(X_e,x_pi)＝minθ_epi；

Wherein, theta_epiThe included angle between the connecting line of the chaser and the escaper and the speed direction of the escaper is formed;

wherein upsilon is_ee'Is the velocity direction vector of the escaper, upsilon_epiConnecting line vector for both chaser and escaper

Velocity of (d);

the distance reduction mechanism comprises:

behavioral trend function

Wherein d is_epi＝|x_e'-x_pi||₂To catch person P_iThe distance to the predicted position E' of the escaper at the next moment;

the structural contraction mechanism comprises:

behavioral trend function

Wherein the content of the first and second substances,

to catch person P_gState quantity of (P)_gTo be able to react with P_iNeighbor individuals, r, of escapes are simultaneously perceived_kThe radius of the circumscribed circle of the kth triangle formed by any three chasers,

is a radius vector, K_rIs the total number of circumscribed circles, and E (r) and σ (r) are the mean and standard deviation, respectively, of the radii of the circumscribed circles, where r is the mean and standard deviation_kThe calculation method is as follows:

wherein, a_k、b_k、c_kThree sides of the kth triangle, A_kIs an edge a_kThe internal angles i, P and q are three vertexes P of a triangle respectively_i、P_p、P_qSubscript of (1), N_sIs P_gTotal number of individuals of (S)_kIs the area of the triangle, C_kThe perimeter of the triangle.

Further, the collision mechanism comprises:

behavioral trend function

Wherein d is_colFor a safe distance, d_ig＝||x_pi-x_pg||₂To catch person P_iAnd P_gDistance of (m)_cIs in the power of the day;

the overlay mechanism includes:

behavioral trend function

Wherein the content of the first and second substances,

in order to be a repulsive force,

in order to have a strong attraction force,

is weak attractive force, xi_fleTo determine the character, xi, for attractive repulsive forces_swMu as a strong or weak attraction determiner_repScaling factor, mu, for repulsive forces_attScaling factor for attractive force, d_fleIs the formation spacing;

in the coverage mechanism, the stable coverage structure is that a chaser cluster takes a regular triangle as a basic coverage unit to contrast an area omega_AUniform coverage is performed at known Ω_AArea S of_AAnd, in case one of the formation spacing or the number of individual clusters is known, another parameter is calculated by the following formula:

wherein, F_sumIn order to cover the required number of faces,

to get the integer operator, S_AIs omega_AArea of (S)_ΔIs the area of the base unit for area coverage;

the edge mechanism includes:

the potential collaborators are judged by the following calculation:

wherein, theta_igTo catch person P_iAnd P_gAngle v based on escaper E_epgTo catch person P_gVector of line connecting with escaper E

Is a vector v_epiAnd upsilon_ee'The outer product of the two phases is,

is vector upsilon_epiAnd upsilon_epiThe outer product between; for P_iIn other words, e.g. theta_ig>θ_epi+ pi/2 and

when is, P_gIs P_iFor P at this time_gIn other words, e.g. theta_ig<N and

when is, P_iIs also P_gPotential collaborators.

Further, the multi-objective optimization function includes:

wherein the content of the first and second substances,

to catch person P_iThe optimum yaw angle of the aircraft is determined,

is a cooperative trend function, where κ is a scale factor and λ ═ λ (λ)_r,λ_d,λ_θ,λ_f) Is a weight vector, V ═ V_r,V_d,V_θ,V_f) As a behavioral trend vector, Ω_coAs a cooperation area, Ω_co,tIn the wake region, the flow of the water is controlled,

for the trend function based on the elimination of wake effects,

is a trend function based on an enhanced distance reduction mechanism, wherein V_d＝exp(d_epi/r_p,cap) -1 is a trend function of the behaviour of the enhanced distance reduction mechanism,

is a region coverage trend function based on the formation distance;

the introduction of the analytic hierarchy process to distribute the weight to the multi-objective optimization function comprises the following steps:

according to the behavior trend vector V ═ V (V)_r,V_d,V_θ,V_f) The sequence of interest of the mechanism involved, lambda_c>λ_r>λ_θ＝λ_dConstructing a decision matrix U, the elements U of which_ijRepresents the influence factor A_iIn A_jThe degree of importance of;

maximum eigenvalue λ of the calculation matrix U_maxAnd its corresponding feature vector v, as the consistency ratio CR<When 0.1, the constructed matrix U passes consistency check;

after normalizing the feature vector, the obtained trend vector V is equal to (V)_r,V_d,V_θ,V_f) The weight distribution scheme of each element is v ═ w₁,w₂,w₃,w₄]^T＝[λ_c,λ_r,λ_θ,λ_d]^T。

Further, the escaper optimization model includes:

wherein phi is^*Optimum yaw angle for the escaper, d_et＝||x_e-x_t||₂The distance between the escaper and the target point,

the escape person and the pursuit person P_jAnd (4) estimating the distance between the positions at the next moment, wherein eta is a relaxation coefficient, and beta is a judgment coefficient of the existence of the chaser.

Further, the particle swarm algorithm comprises:

setting the particle size N, the dimension d of the parameter to be optimized and the maximum iteration number N_iter(ii) a The velocity and position are updated by the following formula:

wherein the content of the first and second substances,

is the velocity of the d-th dimension in which the particle h is located at time instant t,

is the position of the d-th dimension of the particle h at time τ, w is the inertial weight, c₁Learning factors for individuals, c₂As a group learning factor, r₁And r₂Random numbers, pbest, all 0 to 1_hdIs the local extreme value of the d-th dimension of the particle h, gbest_dIs the global extremum for the d-th dimension.

The invention has the beneficial effects that: the cluster distributed capture method based on the multi-mechanism combination strategy in the embodiment realizes a mechanism modularized capture algorithm taking behavior trend as guidance, has simpler and more vivid behavior strategy compared with the existing differential chess playing and geometric method, does not need complex modeling derivation, has simple and convenient algorithm and rapid operation, does not need complex hyper-parameter adjustment and long-time training process, and has rapid deployment capability; the method has higher robustness, adaptivity and expansibility, and can exert task capability superior to centralized control under the condition of limited communication and processing capability; the method has better practical application potential, and the constructed model has higher solving speed under the resolving of the particle swarm algorithm, and can meet the real-time requirement.

Drawings

FIG. 1 is a flowchart of a cluster distributed capture method based on a multi-mechanism combination policy in an embodiment;

FIG. 2 is a detailed flowchart of the confrontation process between the catcher and the escaper in the embodiment;

FIG. 3 is a schematic diagram of the confrontation scenario of both the chaser and the escaper in the embodiment

Fig. 4 is a schematic core mechanism diagram of a cluster distributed capture method based on a multi-mechanism combination policy in the embodiment;

FIG. 5 is a schematic diagram of a wake mechanism of a cluster distributed capture method based on a multi-mechanism combination policy in the embodiment;

FIG. 6 is a diagram illustrating an overlay mechanism and a collaborative enclave mode in an embodiment;

FIG. 7 is a diagram illustrating a driving function of the overlay mechanism in an embodiment;

fig. 8 is an edge mechanism diagram of a cluster distributed capture method based on a multi-mechanism combination policy in the embodiment;

FIG. 9 is a diagram showing a simulation result of the countermeasure process in the embodiment;

FIG. 10 is a graph of convergence efficiency of particle swarm optimization applied in the examples;

FIG. 11(a) is a graph of the success rate based on the speed ratio and the formation pitch obtained by the simulation process in the example;

FIG. 11(b) is a graph of collision rate based on speed ratio and formation pitch obtained by the simulation process in the example;

fig. 12 is a comprehensive performance thermodynamic diagram of the chaser cluster obtained by the simulation process in the embodiment.

Detailed Description

In this embodiment, referring to fig. 1, the cluster distributed capture method based on the multi-mechanism combination policy includes the following steps:

s1, constructing a confrontation scene of a chaser and an escaper;

s2, establishing a kinematics model of the chaser and the escaper;

s3, constructing a multi-mechanism catching strategy of the chaser according to the confrontation scene and the kinematics model;

s4, constructing a multi-objective optimization function according to a multi-mechanism catching strategy of a chaser, and distributing weights for the multi-objective optimization function by introducing an analytic hierarchy process;

s5, solving the multi-target optimization function by using a particle swarm algorithm, and outputting a solving result as a strategy of the chaser;

s6, constructing an escaper optimization model by a manual potential field method;

and S7, solving the optimized model of the escaper by using a particle swarm algorithm, and outputting a solving result as a strategy of the escaper.

In this embodiment, the steps S1-S7 may be executed by a computer. Specifically, all of the steps S1-S7 may be performed by the same computer, where the computer may perform all of the steps S1-S7, may perform only the steps S1-S5, or may perform only the steps S6-S7 after performing the steps S1-S5. Since both the catcher and the escaper are intelligent, the steps related to the catcher in steps S1 to S7 may be executed by the catcher, and the steps related to the escaper in steps S1 to S7 may be executed by the escaper.

In step S1, a confrontation scenario between the chaser and the escaper is constructed. Specifically, the confrontation scene may be formed of the following set parameters:

pursuing person P _i1,2,3,.., N, escaper E, starting point (x)_start,y_start) Target point (x)_target,y_target) And a countermeasure area Ω_A；

The maximum speed v of the chaser_p,maxThe maximum velocity of the escaper is v_e,maxBoth running at maximum speed and having v_p,max<v_e,max；

The number of the chaser individuals is N, the number of the escaper individuals is 1, and N is more than 1;

the perception radius of the chaser is r_p,maxRadius of perception of escaper is r_e,maxHas r of_p,max＝r_e,maxAnd both the pursuit and the evasion parties can acquire the position coordinates and the speed vectors of the individuals of the opposite party in the self-perception range through perception;

the maximum angular velocity of the chaser is limited to omega_p,maxThe maximum angular velocity of the escaper is limited to ω_e,maxHas omega_p,max＝ω_e,max；

The chaser has communication distance limit with r as communication radius_p,comHas r of_p,com＝2·r_p,maxAnd the chaser can mutually acquire position coordinates and speed vectors with neighbors in a communication range;

the arresting radius of the chaser is r_p,capThe warning radius of the escaper is r_alert。

In executing step S1, (x) may be generated in the memory of the computer_start,y_start)、(x_target,y_target) And the variables can store specific numerical values, so that parameters of the chaser and the escaper are described through a plurality of variables, and a confrontation scene is formed.

In step S2, kinematic models of the chaser and the escaper are established. Specifically, the kinematic model may refer to the motion constraint conditions in the confrontation scenario established by the chaser and the escaper at step S1, including the equation between their positions, velocities, angular velocities, and the like. In this embodiment, step S2 may establish the following kinematic model:

wherein x is_pi＝(x_pi,y_pi) To catch person P_iV coordinates of_piTo catch person P_iSpeed of (e), ω_piTo catch person P_iThe angular velocity of (a) of (b),

to catch person P_iYaw angle of, chasing person P_iIs expressed as

v_pi∈[0,v_p,max]，|ω_pi|≤ω_p,max；x_e＝(x_e,y_e) As the coordinate of the escaper E, v_eSpeed of the escaper E, ω_eThe angular velocity of the escaper E, phi is the yaw angle of the escaper E, and the state quantity of the escaper E is represented as X_e＝{x_e,y_e,φ}，v_e∈[0,v_e,max]，|ω_e|≤ω_e,max。

In the following steps S3-S7, steps S3-S5 are actually detailed procedures for decision-making on the side of the chaser under the motion condition constrained by step S2 in the confrontation scene constructed in step S1; steps S6-S7 are actually detailed procedures for decision-making on the side of the escaper under the motion condition constrained by step S2 in the confrontation scene constructed by step S2. The principle of steps S3-S7 is shown in FIG. 2.

Referring to fig. 2, for the catcher cluster, the specific execution strategy when executing steps S3-S5 is:

detecting whether an escaper exists, if so, executing an edge mechanism, and if not, executing a covering mechanism;

when executing the edge mechanism, firstly judging whether the edge mechanism is positioned at the cluster boundary, if so, continuously judging whether a potential partner exists, if so, starting to enter a core mechanism, and if not, executing a covering mechanism;

when a core mechanism is executed, firstly, judging whether the number of collaborators in the collaboration area is more than or equal to two so as to form a polygon with the collaborators, if the number of the collaborators is less than two, not executing a structure contraction mechanism, but only executing a distance reduction mechanism, an angle reduction mechanism and a collision avoidance mechanism, if the number of the collaborators is not less than two, further judging whether the collaborators are in a wake flow area, if the collaborators are in the wake flow area, not executing the distance reduction mechanism, but only executing the structure contraction mechanism, the angle reduction mechanism and the collision avoidance mechanism, otherwise, executing all the mechanisms;

after passing through the core mechanism, weight distribution is carried out on each sub-mechanism by adopting an AHP method, a comprehensive objective function is constructed, the PSO algorithm is utilized for solving, and the optimal yaw angle is generated to be output as a real-time strategy.

Referring to fig. 2, the catching effect of the chaser can be verified by the escaper, and the specific execution strategy when the escaper executes steps S6-S7 is:

detecting whether a chaser exists or not, if so, entering an escape mode, constructing an artificial potential field environment according to the detected chaser, constructing a target function, solving by utilizing a PSO (particle swarm optimization) algorithm, generating an optimal yaw angle as a real-time strategy output, and if not, continuing moving towards a target point.

In this embodiment, the confrontation scenario established in step S1 may be as shown in fig. 3, and steps S3-S7 are specifically described based on the confrontation scenario shown in fig. 3.

In step S3, a multi-mechanism capture strategy is constructed for the chaser according to the confrontation scene and the kinematic model. Specifically, the constructed catcher multi-mechanism catching strategy comprises a core mechanism and an auxiliary mechanism.

In this embodiment, to meet the requirement of the active capture function of the chaser cluster, the core mechanism includes three sub-mechanisms, namely an angle reduction mechanism, a distance reduction mechanism, and a structure contraction mechanism. The principle of the core mechanism is shown in fig. 4. In FIG. 4(a), the angle reduction mechanism drives the chaser individual to move to the front of the escaper for blocking, so that the included angle θ is formed_epiReducing; the distance reduction mechanism drives the pursuit individual to reduce the distance between the pursuit individual and the escaper, so that the distance d_epiReducing; while FIGS. 4(b) and 4(c) show that the mechanism of structural contraction will be driven at Ω_coThe chasers in the area have a tendency to change from 4(b) to 4 (c); FIG. 4(d) shows the action of the entire core mechanism. Omega_coThe area indicates that all chasers in the area can sense the escapers, and the chasers communicate information.

(A1) In this embodiment, the sub-mechanism of the angle reduction mechanism is described by the following equation:

behavior trend function V_θ(X_e,x_pi)＝minθ_epi；

Wherein, theta_epiThe included angle between the connecting line of the chaser and the escaper and the speed direction of the escaper is formed;

wherein upsilon is_ee'Is the velocity direction vector of the escaper, upsilon_epiConnecting line vector for both chaser and escaper

A speed of the motor;

(A2) in this embodiment, the distance reduction mechanism, i.e., the sub-mechanism, is described by the following equation:

behavioral trend function

Wherein d is_epi＝||x_e'-x_pi||₂To catch person P_iThe distance to the predicted position E' of the escaper at the next moment;

(A3) in this embodiment, the sub-mechanism of the structure contraction mechanism is described by the following equation:

behavioral trend function

Wherein the content of the first and second substances,

to catch person P_gQuantity of state of (P)_gTo be able to react with P_iNeighbor individuals, r, of escapes are simultaneously perceived_kThe radius of the circumscribed circle of the kth triangle formed by any three chasers,

is a radius vector, K_rIs the total number of circumscribed circles, and E (r) and σ (r) are the mean and standard deviation, respectively, of the radii of the circumscribed circles, where r is the mean and standard deviation_kThe calculation method is as follows:

wherein, a_k、b_k、c_kThree sides of the kth triangle, A_kIs an edge a_kThe internal angles i, P and q are three vertexes P of a triangle respectively_i、P_p、P_qSubscript of (1), N_sIs P_gTotal number of individuals of (1), S_kIs the area of the triangle, C_kThe perimeter of the triangle.

As shown in fig. 4(b), when it is at Ω_coIn the cooperative chasers in the area, any three chasers can form a triangle and must have a circumcircle. The structure contraction mechanism makes the circumscribed circle of each triangle tend to the mean value of the circumscribed circle set and show a reduction trend by minimizing the radius of the circumscribed circle of all the triangles, eliminates the difference between the circumscribed circles of each triangle, namely reduces the standard deviation of the circumscribed circle set as much as possible, and finally can ensure that the value is in omega_coWherein randomly scattered chasers tend to form a regular polygonal enclosure with the escapers as the center, and continuously shrink to complete the cooperative catching task.

In addition, in order to improve the dynamic stability of the structure contraction mechanism, a wake mechanism is designed to accelerate the cooperative chaser in a cooperative region omega_coInner update iteration as shown in fig. 5. When the chaser is in the wake region omega_co,tI.e. theta_epi>θ_tailThe chaser will not have the distance reduction mechanism and will be expelled through the arc AA' into the region omega under the action of the speed difference between the opposing parties_coThe problem that the chaser clusters are gathered at the tail of the escaper due to the speed difference is solved, and the omega is favorable for_coThe internal structure contracts the mechanism.

In this embodiment, in order to give good cooperative capture conditions to the core mechanism, the auxiliary mechanism includes three sub-mechanisms, namely, a collision mechanism, an overlay mechanism, and an edge mechanism. Wherein, the collision prevention mechanism prevents the collision inside the chaser cluster, especially the collision prevention when the core mechanism acts; the covering mechanism drives the catcher cluster to be converted from the initial random position state to the uniform covering omega_AThe state of the area, the coverage density of which is controlled by the formation pitch; the edge mechanism judges whether potential collaborators exist at the edge of the cluster, if so, the edge mechanism enters the core mechanism, if not, the queue form interval is maintained, and evacuees are induced to go deep into the cluster to capture.

(B1) In this embodiment, the sub-mechanism of the collision mechanism is described by the following equation:

behavioral trend function

Wherein d is_colFor a safe distance, d_ig＝||x_pi-x_pg||₂To catch person P_iAnd P_gDistance of (m)_cIs in the power of the day;

(B2) in this embodiment, the detailed design of the sub-mechanism, i.e. the collision mechanism, is as follows:

based on the same virtual force, the coverage of the area by the cluster should be uniform, i.e. the area tends to be tiled and filled with the same basic polygon module. When the perimeter of the basic polygon is fixed, namely the cluster density/formation space is fixed, the coverage area of the regular polygon is maximum. Assuming that the regular polygon of the base has M sides, the internal angle is pi (M-2)/M, and since the planar tiling is required, the internal angle and the circumferential angle 2 pi should be integer division, i.e. 2M/(M-2) should also be integer. Thus, M can take on values of 3, 4, 6. When M is 6, the polygon is a regular hexagon, and actually is a combination of six regular hexagons; when M is 4, the distance between any two vertexes is inconsistent, and the stability is insufficient; thus, the base polygon for planar overlay is a regular triangle. Fig. 6(a) shows a cluster area coverage pattern. Aiming at the problem that one vertex can be added with two sides of one surface or two surfaces and three sides of two surfaces, the core module and the combined module are arranged, the core module (6 vertexes, 4 surfaces and 8 sides) are used as the center, and the whole spliced combined module (2 vertexes, 3 surfaces and 5 sides) covers the game area. When the area of the game area and the preset formation space are known, the required number of individuals can be calculated; or the required formation spacing can be obtained when the area and cluster size are known.

In the area coverage mode, the calculation relationship between the vertex and the surface is as follows:

in the above formula, V_sumAnd F_sumTotal number of vertices and faces, V, respectively_cAnd F_cRespectively the number of vertices and the number of facets in the core module, V_s,addAnd F_s,addNumber of peaks and faces, Q, added separately to a single combined module_sThe number of the combined modules is the same as the number of the combined modules,

to take down the integer operator. In addition, V_c＝6，F_c＝4，V_s,add＝2，F_s,add＝3。

In the covering mechanism, the stable covering structure is that the catcher cluster takes regular triangles as basic covering units to contrast the area omega_AUniform coverage is performed at known Ω_AArea S of_AAnd, in case one of the formation spacing or the number of individual clusters is known, another parameter is calculated by the following formula:

in the above formula, F_sumIn order to cover the required number of faces,

to get the integer operator, S_AIs omega_AArea of (S)_ΔIs the area of the base unit for area coverage.

In area coverage, when the cluster density is the formation spacing d_fleIn case of change, the cooperation region Ω_coThe number of individuals inside will change as shown in fig. 6 (b). Can be combined with_fleIs specifically divided into [1,3 ]]、[3,4]And [4,6]Three cases for each partner, calculated as:

and

and use it as d_fleOf three segmentation points, wherein r_coIs omega_coOf (c) is used.

The overlay mechanism behavior trend function is as follows:

in the above formula, the first and second carbon atoms are,

in order to be a repulsive force,

in order to have a strong attraction force,

is weak attractive force, xi_fleTo determine the character, xi, for attractive repulsive forces_swMu as a strong or weak attraction determiner_repAnd mu_attScaling factors for repulsive and attractive forces, respectively, d_fleIs the formation pitch. Each virtual force drive function is shown in fig. 7.

(B3) In this embodiment, the sub-mechanism is an edge mechanismIntended as shown in fig. 8. For P_iIn other words, when P is_gIn the potential cooperation area omega_pciWhen is, P_gIs P_iThe potential collaborators can execute corresponding core mechanisms to capture the escapers; when P is_gAt omega_co\Ω_pciAnd in the process, the escapers are considered to be still beyond the edge of the cluster, and each chaser keeps the formation distance, so that the self threat is reduced, and the escapers are attracted to go deep into the cluster.

The potential partner judgment is calculated by the following formula:

in the above formula, [ theta ]_igTo catch person P_iAnd P_gAngle v based on escaper E_epgTo catch person P_gVector of line connecting with escaper E

And

are respectively vector upsilon_epiAnd upsilon_ee'、υ_epiThe outer product between. For P_iIn other words, e.g. theta_ig>θ_epi+ π/2 and

when is, P_gIs P_iPotential collaborators of (a); at this time for P_gIn other words, e.g. theta_ig<N and

when is, P_iIs also P_gPotential collaborators.

In step S4, a multi-objective optimization function of the chaser, that is, a multi-objective optimization function, is constructed according to the multi-mechanism capture strategy of the chaser, which is constructed in step S3 and composed of the angle reduction mechanism, the distance reduction mechanism, the structure contraction mechanism, the collision mechanism, the coverage mechanism, the edge mechanism, and the like. Specifically, the multi-objective optimization function may be represented by the following formula:

wherein the content of the first and second substances,

to catch person P_iThe optimum yaw angle of the aircraft is determined,

is a cooperative trend function, where κ is a scale factor and λ ═ λ (λ)_r,λ_d,λ_θ,λ_f) Is a weight vector, V ═ V_r,V_d,V_θ,V_f) As a behavioral trend vector, Ω_coAs a cooperation area, Ω_co,tIn the wake region, the flow of the water is controlled,

for the trend function based on the elimination of wake effects,

is a trend function based on an enhanced distance reduction mechanism, wherein V_d＝exp(d_epi/r_p,cap) -1 is a trend function of the behaviour of the enhanced distance reduction mechanism,

is a function of the area coverage trend based on the formation distance.

In step S4, when the introduced analytic hierarchy process is executed to assign weights to the multi-objective optimization function, the following steps may be specifically executed:

according to the behavior trend vector V ═ V (V)_r,V_d,V_θ,V_f) The sequence of interest of the containing mechanism lambda_c>λ_r>λ_θ＝λ_dConstructing a decision matrix U, the elements U of which_ijRepresents the influence factor A_iIn A_jThe degree of importance of;

maximum eigenvalue λ of the calculation matrix U_maxAnd its corresponding feature vector v, as the consistency ratio CR<When 0.1, the constructed matrix U passes consistency check;

after normalizing the feature vector, the obtained trend vector V is equal to (V)_r,V_d,V_θ,V_f) The weight distribution scheme of each element is v ═ w₁,w₂,w₃,w₄]^T＝[λ_c,λ_r,λ_θ,λ_d]^T。

And executing the step S5 aiming at the multi-objective optimization function, and solving the multi-objective optimization function by using a particle swarm optimization algorithm to obtain a solution result as the strategy output of the chaser. Specifically, the pellets used in step S5A subgroup algorithm, wherein the particle size N, the dimension d of a parameter to be optimized and the maximum iteration number N are set_iterAfter waiting for the parameters, the speed and position are updated by the following formula:

wherein the content of the first and second substances,

is the velocity of the d-th dimension in which the particle h is located at time instant tau,

is the position of the d-th dimension of the particle h at time τ, w is the inertial weight, c₁Learning factors for individuals, c₂As a group learning factor, r₁And r₂Random numbers, pbest, all 0 to 1_hdIs the local extreme value of the d-th dimension of the particle h, gbest_dIs the global extremum for the d-th dimension.

The result of performing the particle swarm algorithm in step S5 is to obtain the optimal yaw angle of the multiple-objective function phi (-) of the chaser at each moment

And (4) outputting the strategy as the pursuit party. Specifically, the computer obtains the optimal yaw angle of the chaser at each moment

Thereafter, the movement of the chaser can be simulated accordingly in the simulation environment, and the movement of the chaser can be controlled accordingly in the actual environment.

In step S6, according to the pursuit multi-mechanism catching strategy composed of the angle reduction mechanism, the distance reduction mechanism, the structure contraction mechanism, the collision mechanism, the coverage mechanism, the edge mechanism, and the like, which is constructed in step S3, a multi-objective escape person optimization function, that is, an escape person optimization model, is constructed through an artificial potential field method. Specifically, the escaper optimization model can be represented by the following equation:

wherein phi is^*Optimum yaw angle for the escaper, d_et＝||x_e-x_t||₂The distance between the escaper and the target point,

the escape person and the pursuit person P_jAnd (4) estimating the distance between the positions at the next moment, wherein eta is a relaxation coefficient, and beta is a judgment coefficient of the existence of the chaser.

And executing the step S7 aiming at the optimum model of the escaper, and solving the multi-objective optimization function by using a particle swarm optimization so as to obtain a solution result as the strategy output of the chaser. Specifically, the particle swarm algorithm used in step S7 is the same as the particle swarm algorithm used in step S5, and is also set for the particle size N, the dimension d of the parameter to be optimized, and the maximum iteration number N_iterAfter waiting for the parameters, the speed and position are updated by the following formula:

wherein the content of the first and second substances,

is the velocity of the d-th dimension in which the particle h is located at time instant tau,

is the position of the d-th dimension of the particle h at time τ, w is the inertial weight, c₁Learning factors for individuals, c₂As a group learning factor, r₁And r₂Random numbers, pbest, all 0 to 1_hdIs the local extreme value of the d-th dimension of the particle h, gbest_dIs the global extremum for the d-th dimension.

The result of executing the particle swarm optimization in step S7 is to obtain the optimal yaw angle phi of the multi-target function psi (-) of the escaper at each moment^*And the strategy is output as the strategy of the escaper side. Specifically, the computer obtains the optimum yaw angle φ of the escaper at each moment^*Then, the motion of the escaper can be simulated under the simulation environment, and the motion of the escaper can be controlled under the actual environment.

By executing steps S1-S5 or S1-S7, the cluster distributed capture method based on the multi-mechanism combination policy in this embodiment can achieve the following technical effects:

(1) compared with the existing differential game and geometric method, the technical means in the embodiment has simpler and more distinct behavior strategy, does not need complex modeling derivation, has simple and convenient algorithm and quick operation, does not need complex hyper-parameter adjustment and long-time training process, and has quick deployment capability;

(2) the distributed interaction mechanism is utilized to utilize local sensing and communication capacity, and by means of the designed simple rule and the local interaction mechanism, the group has higher robustness, self-adaptability and expansibility, and can exert task capacity superior to centralized control under the condition of limited communication and processing capacity;

(3) the intelligent sensing range, the communication range and the steering maneuverability limit are considered by combining with actual conditions, the method has better practical application potential, and the constructed model is fast in solving speed under the resolving of the particle swarm algorithm, so that the real-time requirement can be met.

In this embodiment, in order to test the effectiveness of the cooperative capture algorithm based on the multi-mechanism combination strategy, relevant simulation verification is performed, and a 20 × 20m barrier-free scene is established in the simulation environment, wherein the game area is a 10 × 10m area framed by a red wire frame, and a chaser cluster is randomly generated in the area. The coordinates of the starting point of the escaper are (2.5 ), and the coordinates of the target point are (17.5 ).

The basic parameter settings of both parties are shown in table 1:

TABLE 1 run-on simulation parameter settings

From the parameters in the table, the speed ratio α ═ v between the chaser and the escaper_p,max/v_e,maxThe ratio of the number of individuals is 15:1, the maximum angular velocity, the radius of perception and the radius of the device are all the same, and the catch radius of the chaser is equal to the alert radius of the escaper. In addition, the hyper-parameter setting in the algorithm is as follows: k is set to 1, λ ═ λ_r,λ_d,λ_θ,λ_f]＝[0.2624,0.1411,0.1411,0.4554]The maximum iteration number of the PSO algorithm is 35, the particle population size is 50, and the speed updating related parameter is [ w, c ]₁,c₂]＝[0.73,1.5,1.5]。

In this embodiment, the algorithm simulation process is as shown in fig. 9, and the result shows that the chaser cluster can finally successfully catch a single high-speed escaper. Specifically, the method comprises the following steps: when t is 0s, the chaser cluster is randomly generated in the game area, and the escaper starts from the starting position; when t is 5s to 15s, the chaser starts to cover the game area under the action of the covering mechanism to prepare for catching; when t is 15s to 20s, the escaper finds that more chasers are in the sensing range of the escaper and searches for the weak direction of the chaser to escape, and the escaper does not enter the inside of the chaser cluster but moves around the edge of the cluster at the moment, so that the maneuvering flexibility of the escaper strategy is embodied; when t is 25s, under the action of an edge mechanism, a chaser at the edge of the cluster does not directly catch an escaper and let the escaper go deep into the cluster; when t is 30s, the core mechanism and the collision avoidance mechanism start to execute, but the escaper has escaped to cooperatively catch the edge of the enclosure ring because the speed of the escaper is high; when t is 35s, the surrounding structure in the previous period smoothly transits to the stage under the action of a wake mechanism, and the surrounding structure in the stage stably and accurately catches the high-speed escaper. Through the analysis, the multi-mechanism combination strategy provided by the work can activate different sub-mechanism combinations under different conditions, so that a chaser cluster can successfully cooperate to catch a single high-speed escaper under the framework of distributed local area communication, meanwhile, a model constructed by the invention has higher convergence efficiency under the resolving of a particle swarm algorithm, and a single-step resolving convergence algebraic statistical graph is shown in a figure 10.

Preferably, in the simulation example, the speed ratio and the formation pitch setting are respectively equal to α and 0.5, and d_fleThe predetermined task can be successfully completed as 3.69. In order to find out the performance domain of the proposed method, the section develops tests in two dimensions of speed ratio and formation spacing based on success rate and collision rate indexes, each data point is subjected to 100 repeated tests, and the results are shown in fig. 11.

In the success rate graph 11(a), the speed ratio ranges from 0.4 to 1.0, with an interval of 0.1; the formation spacing is from 2.0 to 5.5, and the interval is 0.5. Analysis shows that the cluster capture success rate increases with the increase of the speed ratio and the power increase decreases with the increase of the speed ratio under the same formation spacing; under the same speed ratio, on the scale of the formation spacing, the success rate is higher in the middle and lower on two sides, and is in a single-peak shape, and along with the increase of the speed ratio, the disadvantage state of the formation spacing of the chaser clusters on two sides or too large or too small is gradually compensated by the increase of the speed. Therefore, when the formation distance is properly selected, the cluster has better capturing capacity. In the collision rate graph 11(b), the speed ratio range is set in accordance with the success rate curve. The collision rate indicates that any individual has a collision event during a single test, and is recorded as a collision. As can be seen from the data diagram, under the same formation pitch, the collision rate increases with the increase of the speed ratio; the smaller the formation pitch, the higher the collision rate at the same speed ratio. Therefore, the larger the formation pitch, the smaller the speed ratio, and the lower the collision rate, but a higher success rate cannot be ensured. Therefore, a comprehensive evaluation index is needed to evaluate the cluster performance, and the optimal formation spacing setting under different speed ratio conditions is found according to the evaluation index.

The formula of the constructed comprehensive evaluation index is shown as follows:

in the above formula, E_h,scFor comprehensive evaluation of the index value, R_s，R_cRespectively indicating success rate and collision rate. E_h,scMeans based on R_cTo R_sThe discount of (1). In particular, when R_cWhen equal to 0, E_h,sc＝R_s。

The cluster performance thermodynamic diagrams presented by the composite evaluation index in the speed ratio and formation pitch dimensions are shown in fig. 12. The darker the color in the graph indicates that the cluster is better in comprehensive performance, i.e., high in power and low in collision rate, and is not good enough otherwise. According to analysis, when d is_fleWhen the speed ratio is 4, the cluster has better performance under each speed ratio; when α is 0.7, the chaser cluster has a wide excellent performance area without a large speed capability. Meanwhile, areas A, B and C in the graph represent a comprehensive performance stable area, namely when data points are located in the area, even if the speed ratio and the formation spacing fluctuate within a certain range in the actual situation, the cluster comprehensive performance does not fluctuate obviously, and the robustness is good. In summary, the best performance region of the strategy proposed in this section is the B region, which is the most suitable for the case where the speed ratio is about 0.7 and the formation pitch is set to 4, and when facing other speed ratio cases, the formation pitch may also be selected to be 4, so as to ensure that the cluster has better comprehensive performance. In addition, in consideration of the bounding mode shown in fig. 6(b), the specific formation interval can be calculated as

Therefore, when Ω_coWhen there are three or four collaborators in the area, the cluster performance is better, and too many or too few collaborators can influence the comprehensive performance of the cluster.

Through the description of the steps and the simulation results shown in fig. 9-12, the invention establishes a distributed capture method based on a multi-mechanism combination strategy by taking the arrival-rejection game in the pursuit game as the scene cut-in and emphasizing the pursuit player cluster, various sub-mechanisms driven by behavior guidance are designed in a modularized way, the cluster capture problem under the manufacture of each sub-mechanism is converted into a multi-objective optimization problem, and the output strategy is solved in real time by utilizing a particle swarm algorithm. The method has simple and clear behavior strategy, does not need complicated modeling derivation, hyper-parameter adjustment and long-time training process, has rapid deployment capability, higher robustness, adaptivity and expansibility, has high algorithm solving speed, and can meet the real-time requirement.

The cluster distributed capture method based on the multi-mechanism combination strategy in the embodiment can be implemented by writing a computer program for implementing the cluster distributed capture method based on the multi-mechanism combination strategy in the embodiment, writing the computer program into a computer device or a storage medium, and when the computer program is read out and operated, implementing the cluster distributed capture method based on the multi-mechanism combination strategy in the embodiment, thereby achieving the same technical effect as the cluster distributed capture method based on the multi-mechanism combination strategy in the embodiment.

It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature or indirectly fixed or connected to the other feature. Furthermore, the descriptions of upper, lower, left, right, etc. used in the present disclosure are only relative to the mutual positional relationship of the constituent parts of the present disclosure in the drawings. As used in this disclosure, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. In addition, unless defined otherwise, all technical and scientific terms used in this example have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in the description of the embodiments herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this embodiment, the term "and/or" includes any combination of one or more of the associated listed items.

It will be understood that, although the terms first, second, third, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element of the same type from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the present disclosure. The use of any and all examples, or exemplary language ("e.g.," such as "or the like") provided with this embodiment is intended merely to better illuminate embodiments of the invention and does not pose a limitation on the scope of the invention unless otherwise claimed.

It should be recognized that embodiments of the present invention can be realized and implemented in computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The methods may be implemented in a computer program using standard programming techniques, including a non-transitory computer-readable storage medium configured with the computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner, according to the methods and figures described in the detailed description. Each program may be implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Furthermore, the program can be run on a programmed application specific integrated circuit for this purpose.

Further, operations of processes described in this embodiment can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described in this embodiment (or variations and/or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) collectively executed on one or more processors, by hardware, or combinations thereof. The computer program includes a plurality of instructions executable by one or more processors.

Further, the method may be implemented in any type of computing platform operatively connected to a suitable interface, including but not limited to a personal computer, mini computer, mainframe, workstation, networked or distributed computing environment, separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, and the like. Aspects of the invention may be embodied in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optically read and/or write storage medium, RAM, ROM, or the like, such that it may be read by a programmable computer, which when read by the storage medium or device, is operative to configure and operate the computer to perform the procedures described herein. Further, the machine-readable code, or portions thereof, may be transmitted over a wired or wireless network. The invention described in this embodiment includes these and other different types of non-transitory computer-readable storage media when such media include instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. The invention also includes the computer itself when programmed according to the methods and techniques described herein.

A computer program can be applied to input data to perform the functions described in the present embodiment to convert the input data to generate output data that is stored to a non-volatile memory. The output information may also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including particular visual depictions of physical and tangible objects produced on a display.

The above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiment, and any modifications, equivalent substitutions, improvements, etc. within the spirit and principle of the present invention should be included in the protection scope of the present invention as long as the technical effects of the present invention are achieved by the same means. The invention is capable of other modifications and variations in its technical solution and/or its implementation, within the scope of protection of the invention.

Claims (10)

1. The cluster distributed capture method based on the multi-mechanism combination strategy is characterized by comprising the following steps:

constructing a confrontation scene of a chaser and an escaper; the chaser and the escaper are both intelligent agents;

establishing a kinematic model of the chaser and the escaper;

constructing a multi-mechanism capture strategy of a chaser according to the confrontation scene and the kinematics model;

constructing a multi-objective optimization function according to the multi-mechanism capture strategy of the chaser, and introducing an analytic hierarchy process to distribute weights for the multi-objective optimization function;

and solving the multi-objective optimization function by using a particle swarm algorithm, and outputting a solving result as a strategy of the chaser.

2. The cluster distributed capture method based on multi-mechanism combination strategy as claimed in claim 1, wherein the cluster distributed capture method based on multi-mechanism combination strategy further comprises:

constructing an optimized model of an escaper by an artificial potential field method;

and solving the optimized model of the escaper by using a particle swarm algorithm to obtain a solution result as the strategy output of the escaper.

3. The multi-mechanism combination strategy-based cluster distributed capture method according to claim 1 or 2, wherein the countermeasure scenario comprises:

catch up person P_i1,2,3,.., N, escaper E, starting point (x)_start,y_start) Target point (x)_target,y_target) And a countermeasure area Ω_A；

The maximum speed v of the chaser_p,maxThe maximum velocity of the escaper is v_e,maxBoth running at maximum speed and having v_p,max<v_e,max；

The number of the chaser individuals is N, the number of the escaper individuals is 1, and N is more than 1;

the perception radius of the chaser is r_p,maxRadius of perception of escaper is r_e,maxIs at a distance of r_p,max＝r_e,maxAnd both the pursuit and the evasion parties can acquire the position coordinates and the speed vectors of the individuals of the opposite party in the self-perception range through perception;

the maximum angular velocity of the chaser is limited to omega_p,maxThe maximum angular velocity of the escaper is limited to ω_e,maxHas omega_p,max＝ω_e,max；

The chaser has communication distance limitation with r as the communication radius_p,comHas r of_p,com＝2·r_p,maxAnd the chaser can mutually acquire position coordinates and speed vectors with neighbors in a communication range;

the arresting radius of the chaser is r_p,capThe warning radius of the escaper is r_alert。

4. The multi-mechanism combination strategy-based cluster distributed capture method according to claim 1 or 2, wherein the kinematic model comprises:

wherein x is_pi＝(x_pi,y_pi) To catch person P_iCoordinate of (v)_piTo catch person P_iSpeed of (e), ω_piTo catch person P_iThe angular velocity of (a) of (b),

to catch person P_iYaw angle of, chasing person P_iIs expressed as

v_pi∈[0,v_p,max]，|ω_pi|≤ω_p,max；x_e＝(x_e,y_e) As the coordinate of the escaper E, v_eSpeed of the escaper E, ω_eThe angular velocity of the escaper E, phi the yaw angle of the escaper E, and the state quantity of the escaper E is represented as X_e＝{x_e,y_e,φ}，v_e∈[0,v_e,max]，|ω_e|≤ω_e,max。

5. The multi-mechanism combination strategy-based cluster distributed capture method according to claim 1 or 2, wherein the chaser multi-mechanism capture strategy comprises a core mechanism and an auxiliary mechanism; the core mechanism includes an angle reduction mechanism, a distance reduction mechanism, and a structure contraction mechanism, and the auxiliary mechanism includes a collision mechanism, an overlay mechanism, and an edge mechanism.

6. The cluster distributed capture method based on the multi-mechanism combination strategy as claimed in claim 5, characterized in that:

the angle reduction mechanism includes:

behavior trend function V_θ(X_e,x_pi)＝minθ_epi；

Wherein, theta_epiThe included angle between the connecting line of the chaser and the escaper and the speed direction of the escaper;

wherein upsilon is_ee'Is the velocity direction vector of the escaper, upsilon_epiConnecting line vector for both chaser and escaper

Velocity of (d);

the distance reduction mechanism comprises:

behavioral trend function

Wherein d is_epi＝||x_e'-x_pi||₂To catch person P_iThe distance to the predicted position E' of the escaper at the next moment;

the structural contraction mechanism comprises:

behavioral trend function

Wherein the content of the first and second substances,

to catch person P_gQuantity of state of (P)_gTo be combined with P_iNeighbor individuals, r, of escapes are simultaneously perceived_kThe radius of the circumscribed circle of the kth triangle formed by any three chasers,

is a radius vector, K_rIs the total number of circumscribed circles, and E (r) and σ (r) are the mean and standard deviation, respectively, of the radii of the circumscribed circles, where r is the mean and standard deviation_kThe calculation method is as follows:

wherein, a_k、b_k、c_kThree sides of the kth triangle, A_kIs an edge a_kThe internal angles i, P and q are three vertexes P of a triangle respectively_i、P_p、P_qSubscript of (2), N_sIs P_gTotal number of individuals of (1), S_kIs the area of the triangle, C_kThe perimeter of the triangle.

7. The cluster distributed capture method based on the multi-mechanism combination strategy according to claim 5, characterized in that:

the collision mechanism includes:

behavioral trend function

Wherein d is_colFor a safe distance, d_ig＝||x_pi-x_pg||₂To catch person P_iAnd P_gM, m_cIs in the power of the day;

the overlay mechanism includes:

behavioral trend function

Wherein the content of the first and second substances,

in order to act as a repulsive force,

in order to have strong attraction force, the air conditioner is provided with a fan,

is weak attractive force, xi_fleIs an attractive repulsive force determiner, ξ_swMu as a strong or weak attraction determiner_repScaling factor, mu, for repulsive forces_attScaling factor for attractive force, d_fleIs the formation spacing;

in the coverage mechanism, the stable coverage structure is that a chaser cluster takes a regular triangle as a basic coverage unit to contrast an area omega_AUniform coverage is performed at known Ω_AArea S of_AAnd, in case one of the formation spacing or the number of individual clusters is known, another parameter is calculated by the following formula:

wherein, F_sumIn order to cover the required number of faces,

to get the integer operator, S_AIs omega_AArea of (S)_ΔIs the area of the base unit for area coverage;

the edge mechanism includes:

the potential collaborators are judged by the following calculation:

wherein, theta_igTo catch person P_iAnd P_gAngle v based on escaper E_epgTo catch person P_gTo escapers ELine vector

Is a vector v_epiAnd upsilon_ee'The outer product of the two phases is,

is a vector v_epiAnd upsilon_epiThe outer product between; for P_iIn other words, e.g. theta_ig>θ_epi+ pi/2 and

when is, P_gIs P_iFor P at this time_gIn other words, e.g. theta_ig<N and

when P is present_iIs also P_gPotential collaborators.

8. The cluster distributed capture method based on the multi-mechanism combination strategy as claimed in claim 1 or 2, characterized in that:

the multi-objective optimization function comprises:

wherein the content of the first and second substances,

to catch person P_iThe optimum yaw angle of the aircraft is determined,

is a cooperative trend function, where κ is a scale factor and λ ═ λ (λ)_r,λ_d,λ_θ,λ_f) Is a weight vector, V ═ V_r,V_d,V_θ,V_f) As a behavioral trend vector, Ω_coAs a cooperation area, Ω_co,tIn the wake region, the flow of the water is controlled,

for the trend function based on the elimination of wake effects,

is a trend function based on an enhanced distance reduction mechanism, wherein V_d＝exp(d_epi/r_p,cap) -1 is a trend function of the behaviour of the enhanced distance reduction mechanism,

is a region coverage trend function based on the formation distance;

the introduction of the analytic hierarchy process to distribute the weight to the multi-objective optimization function comprises the following steps:

according to the behavior trend vector V ═ V (V)_r,V_d,V_θ,V_f) The sequence of interest of the mechanism involved, lambda_c>λ_r>λ_θ＝λ_dConstructing a judgment matrix U, the elements U of which_ijRepresents the influence factor A_iTo A_jThe degree of importance of;

maximum eigenvalue λ of the calculation matrix U_maxAnd its corresponding feature vector v, as the consistency ratio CR<When 0.1, the constructed matrix U passes consistency check;

after the feature vector is normalized, the obtained trend vector V is equal to (V)_r,V_d,V_θ,V_f) The weight distribution scheme of each element is v ═ w₁,w₂,w₃,w₄]^T＝[λ_c,λ_r,λ_θ,λ_d]^T。

9. The multi-mechanism combination strategy-based cluster distributed capture method according to claim 2, wherein the escaper optimization model comprises:

wherein phi^*Optimum yaw angle for the escaper, d_et＝||x_e-x_t||₂The distance between the escaper and the target point,

the escape person and the pursuit person P_jAnd (4) estimating the distance between the positions at the next moment, wherein eta is a relaxation coefficient, and beta is a judgment coefficient of the existence of the chaser.

10. The multi-mechanism combination strategy based cluster distributed capture method according to claim 1 or 2, wherein the particle swarm algorithm comprises:

setting the particle size nDimension d of parameter to be optimized, maximum number of iterations N_iter(ii) a The velocity and position are updated by the following formula:

wherein the content of the first and second substances,

is the velocity of the d-th dimension in which the particle h is located at time instant tau,

is the position of the d-th dimension of the particle h at time τ, w is the inertial weight, c₁Learning factors for individuals, c₂As a group learning factor, r₁And r₂Random numbers, pbest, all 0 to 1_hdIs the local extreme value of the d-th dimension of the particle h, gbest_dIs the global extremum for the d-th dimension.

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